Questions: Calculation-based problems (please use PSW). 6. ( 20 pts ) A dog (23.0-kg) is riding in an elevator which is moving upward, Ignore any resistance. (a) Determine the acceleration of the elevator, when the normal force from the elevator to the dog is 252.5 N. (b) Determine the normal force from the elevator to the dog, when the elevator is slowing down at a rate of 0.87 m / s^2.

Solution Steps

We need to determine the acceleration of the elevator and the normal force acting on the dog under different conditions. The mass of the dog is given as \( m = 23.0 \, \text{kg} \).

We are given the normal force \( F_N = 252.5 \, \text{N} \) and need to find the acceleration \( a \) of the elevator.

Using Newton's second law: \[ F_N = m(g + a) \]

Where:

• \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity)
• \( m = 23.0 \, \text{kg} \)

Rearranging to solve for \( a \): \[ a = \frac{F_N}{m} - g \]

Substituting the given values: \[ a = \frac{252.5 \, \text{N}}{23.0 \, \text{kg}} - 9.81 \, \text{m/s}^2 \] \[ a = 10.9783 \, \text{m/s}^2 - 9.81 \, \text{m/s}^2 \] \[ a = 1.1683 \, \text{m/s}^2 \]

We are given the deceleration \( a = -0.87 \, \text{m/s}^2 \) and need to find the normal force \( F_N \).

Using Newton's second law: \[ F_N = m(g + a) \]

Substituting the given values: \[ F_N = 23.0 \, \text{kg} \times (9.81 \, \text{m/s}^2 - 0.87 \, \text{m/s}^2) \] \[ F_N = 23.0 \, \text{kg} \times 8.94 \, \text{m/s}^2 \] \[ F_N = 205.62 \, \text{N} \]

Final Answer